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%I #11 Apr 05 2014 17:57:43
%S 1,3,10,128,201,223,246,309,357,393,424,482,526,815,887,909,1014,1196,
%T 1543,1610,1653,1674,1743,2219,2302,2339,2371,2475,2513,2611,2948,
%U 3107,3273,3419,3434,3516,3555,3593,4070,4203,4288,4332,4389,4428,4724,4793
%N Numbers n such that both the difference and the sum of (n-th prime+1)^2 and (n-th prime)^2 are prime.
%F a(n) = Pi(A098717(n)) = A049084(A098717(n)). - _R. J. Mathar_, Mar 09 2010
%e a(1)=1 because (1st prime+1)^2 - (1st prime)^2=5 is prime and (1st prime+1)^2 + (1st prime)^2=13 is prime;
%e a(2)=3 because (3rd prime+1)^2 - (3rd prime)^2=11 is prime and (3rd prime+1)^2 + (3rd prime)^2=61 is prime;
%e a(3)=10 because (10th prime+1)^2 - (10th prime)^2=59 is prime and (10th prime+1)^2 + (10th prime)^2=1741 is prime;
%e a(4)=128 because (128th prime+1)^2 - (128th prime)^2=1439 is prime and (128th prime+1)^2 + (128th prime)^2=1035361 is prime.
%t npsQ[n_]:=Module[{np=Prime[n],a,b},a=np^2;b=(np+1)^2;And@@PrimeQ[ {a+b,b-a}]]; Select[Range[5000],npsQ] (* _Harvey P. Dale_, Sep 11 2011 *)
%Y Cf. A000040, A068501.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Mar 01 2010
%E Extended beyond a(4) by _R. J. Mathar_, Mar 09 2010
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